Olvido, A. E., and L. S. Blumer. 2005. Introduction to mark-recapture

This article reprinted from:

Olvido, A. E., and L. S. Blumer. 2005. Introduction to mark-recapture census methods

using the seed beetle, Callosobruchus maculatus. Pages 197-211, in Tested Studies for

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197

Chapter 11

Introduction to Mark-Recapture Census Methods

Using the Seed Beetle, Callosobruchus maculatus

Alexander E. Olvido

and Lawrence S. Blumer

Department of Biology,

Virginia State University,

Petersburg, VA 23806

[email protected]

Department of Biology,

Morehouse College,

830 Westview Drive, S.W.

Atlanta, GA 30314

[email protected]

Alex Olvido received his B.Sc. from the University of California at Irvine and Ph.D.

from the University of South Carolina at Columbia. Alex co-authored this laboratory

study while working as a post-doctoral research scientist under the supervision of Dr.

Larry Blumer. A newly minted assistant professor at Virginia State University, Alex

now teaches both majors and non-majors introductory biology and pursues his

research interests concerning the evolution of sexual signals and mating preferences

of crickets and related insects.

Larry Blumer earned his graduate and undergraduate degrees from the University of

Michigan, and he is currently Associate Professor of Biology at Morehouse College.

His teaching interests are in the areas of Ecology, Environmental Biology, and

Evolution and Behavior. His research interests are in the same fields, and include

recent studies on the neurobiology of mate choice in fishes and insects and the

neuroendocrine correlates of social stress in fishes.

198 Mark-recapture census of C. maculatus populations

Contents

Introduction 198

Student Outline

Objectives 199

Introduction 199

Methods 201

Data Analysis 201

Points to Ponder 202

Literature Cited (Student Outline) 202

Appendix A: Building Poisson 95% Confidence Intervals 203

Appendix B: Correction for Small Sample Size 204

Appendix C: Accuracy Versus Precision 204

Materials 205

Notes to the Instructor 205

Culturing Callosobruchus maculates 205

Marking Techniques 206

Containment Issues 207

Probable Causes of Sampling Bias 208

One Final Tip 211

Literature Cited (Notes to the Instructor) 211

Acknowledgements 211

Introduction

Population size, or the abundance of organisms in a study site, is the most fundamental of the

primary demographic statistics. Here, we present a laboratory study that introduces college

undergraduates to mark-recapture methods that estimate population size. At Morehouse College,

students conduct this study in a junior/senior level ecology course, but the study can easily be

modified for students at the introductory level. The level of mathematical sophistication in this

exercise is low, requiring only that students perform simple algebra. Students apply a simple mark-

recapture technique to estimate population size in cultures of a seed beetle, Callosobruchus

maculatus. After completing this study, students not only gain rudimentary knowledge of statistical

methods, e.g., standard deviation and 95% confidence limits, but also learn how to assess the

reliability of population-size estimates.

Mark-recapture census of C. maculatus populations

199

Student Outline

Objectives

1. Learn the mathematical methodology for estimating population size in nature by means of

mark-recapture techniques.

2. Perform an experiment to estimate the number of adults in a series of bean beetle cultures

and to evaluate the reliability of the estimations.

Introduction

Estimating the abundance of organisms, especially in naturally occurring populations, is a

fundamentally important activity in ecological research. An accurate census informs us of changes

in population size due to migrations into or out of our sampling sites, as well as to season-related

recruitment (births) and mortality (deaths). There are many ways to perform a population census,

and each method makes certain assumptions about the population. In this study, we will use a

census method known as “mark-recapture” and learn about those assumptions.

Mark-recapture techniques allow ecologists to track movement of individuals in space and in

time through a population. Data from mark-recapture experiments are so important that researchers

continue refining analytical techniques to maximize the information yield from mark-recapture data

(Lebreton et al., 1992; Schwarz and Seber, 1999; Schtickzelle et al., 2003). Here, we briefly

describe three basic mark-recapture methods: the Petersen, the Schnabel, and the Jolly-Seber

methods.

The Petersen method, also known as the Lincoln index (Haag & Tonn, 1998), is the easiest of the

mark-recapture census methods to perform because it is based on single episode of marking and

recapturing individuals (Table 1). The important assumptions of the Petersen method are:

1. The population being sampled is closed (no births/deaths/migration) so that population

size remains constant throughout the sampling period.

2. Every individual has the same chance of being caught; in other words, sampling is

random.

3. Marks are not lost in the interval between mark and recapture.

Population estimation with the Petersen method is based on equivalent ratios such that the

proportion of the population that is marked and released will be the same as the proportion of

individuals in a recapture sample that were previously marked:

Total number marked in population (M)

Total number estimated in population (N)

Number found marked in recapture sample (R)

Total number in recapture sample (C)

In contrast, the Schnabel method requires successive episodes of recapture; yet, like Petersen, the

Schnabel method requires only a single episode of marking (Table 1). That is, individuals are

marked at first capture, and no further marking is required even with subsequent recaptures. While it

makes the same assumptions as in Petersen, the Schabel method’s reliance on multiple sampling

episodes makes it particularly sensitive to violations of the assumptions noted in the Petersen

method.

200 Mark-recapture census of C. maculatus populations

Often, ecologists cannot study closed, constant-sized populations. The Jolly-Seber (JS)

method was developed specifically to study demographic patterns of natural, or open, populations.

Like Schnabel, the JS method involves successive episodes of capture. However, JS also requires

that the census-taker keep track of when an individual from a study population was last caught, i.e. at

the very least, marks must correspond to a unique time of capture for each recaptured individual.

Although the most challenging logistically and mathematically, the JS method is also the most

informative of the three mark-recapture census methods described thus far: JS estimates not only

population size, but also persistence rate (i.e. survival and site fidelity combined) from a group of

marked individuals. Aside from the assumption of an open population, the JS method assumes that:

1. Every individual has the same chance of being captured at each sampling.

2. Marks are not lost during the entire census period.

Table 1. Summary of three basic mark-recapture census methods.

Method # of recapture events # of marking events

Petersen single single

Schnabel multiple single

Jolly-Seber multiple multiple

The Importance of Randomness

A central element in all three mark-recapture census methods is the notion that populations are

sampled in random fashion. However, what exactly is “random?” For our purposes, randomness

means that each individual in the study population has the same (or nearly the same) probability of

being captured, so that each sampling event has no effect on previous sampling events. In applying

Petersen mark-recapture techniques, we not only presume that (1) recapture rate reflects the

underlying spatial distribution in the study population, i.e. homogeneously distributed individuals,

but also assume (2) our manner of sampling is itself random. Violation of either of these

assumptions leads to biased estimates of population size.

On Reliability of Estimated Counts

Regardless of census method, ecologists should always evaluate the reliability of their

population-size estimates. Why? An estimate, by definition, carries with it a level of uncertainty, so

that one population-size estimate could very well be as (un)informative as another could. Hence,

instead of relying on a single estimate of population size, ecologists construct a range of estimates

known as a “confidence interval.” A confidence interval of our estimated population size (N

EST

), is

a numerical range within which the actual, or true, population size (N

TRUE

) will fall with a certain

level of probability (Sokal and Rohlf, 1981). For example, a 95% confidence interval of N

EST

is one

in which the experimenter specifies the width of a series of confidence intervals, such that 95 of 100

intervals contain N

TRUE

. Population-size estimates belonging to the same confidence interval have

an equal chance of representing the true population size. In ecology, the de facto standard level for

confidence intervals is 95 per cent, i.e. a 95% confidence interval fitted around our point estimate of

population size.

In this study, you will apply the Petersen method to obtain point estimates of population size in a

stock of cowpea seed beetle, Callosobruchus maculatus (Coleoptera: Bruchidae). You will then

Mark-recapture census of C. maculatus populations

201

evaluate their reliability by fitting 95% confidence intervals around those point estimates, and later

comparing your point estimates against the actual number of beetles in your study population.

Bean beetles, Callosobruchus maculatus, are agricultural pest insects originating from Africa

and Asia. Females lay their eggs singly on the surface of beans (Family Fabaceae). After several

days, the beetle larva hatches out and burrows into the bean. At 30

C, pupation and emergence of

an adult beetle occurs 25-30 days after oviposition. Adults mature 24-36 hours after emergence, and

they appear not to feed. Adults may live for about 12 days, in which time females mate and oviposit.

Brown and Downhower (1988) provide more information on the natural history of C. maculatus.

Methods

Each group of students will receive a petri dish filled with a single layer of mung beans and some

beetles. Each group should mark a pre-determined number of live beetles in the colony dish

provided, e.g. mark 20 or more live beetles – ignore the dead ones – and then use a flat toothpick to

apply nail polish to that number of beetles. Apply a small drop (or dot) to the back of the beetle’s

thorax, and avoid painting the wing covers since C. maculatus beetles are agile enough to wipe off

paint from this area. Divide the counting and marking workload equally among group members.

Note the exact number of beetles that you’ve marked, and then allow marked beetles to hide

(“disperse”) among the mung beans and unmarked individuals in the colony dish. You and your lab

partner(s) are now ready to estimate population size in your colony dish.

Using soft forceps, each person in your group should be allowed exactly two minutes to

withdraw randomly as many beetles (both marked and unmarked) as possible from your group’s

petri dish. At the end of each person’s sampling, count the number of marked and unmarked beetles

that were withdrawn, and then return the sampled beetles to the petri dish. Each person in your

group should repeat the sampling from this same petri dish. You can check the accuracy of your

counting by noting that the number of marked and unmarked beetles should sum to the total number

of beetles captured (Table 2).

Table 2. A template for tallying each person’s count.

Name of person sampling

Total number of beetles captured (C)

Number of marked beetles captured (R)

Number of unmarked beetles captured

Data Analysis

Estimate the total number of beetles in your study population. Use the following symbols to

organize your data (after Krebs, 1989):

M = number of individuals marked and released

C = total number of individuals captured (in the recapture sample)

R = number of individuals in the recapture sample that are marked

EST

= your estimate of the total population size

202 Mark-recapture census of C. maculatus populations

As you already know,

EST

, so that the reciprocal,

EST

, is also true. We can then

re-arrange the equation to obtain the estimated total population size:

EST

M  C

This calculation can be performed in a Microsoft

Excel

spreadsheet titled “PopEst.xls”

located on the Ecology laboratory computers. PopEst.xls will also calculate the 95% confidence

limits for your point estimate of total population size (see Appendix A).

Once you have made your calculations, you and the members of your group will need to assess

the accuracy (as distinct from precision, and explained in Appendix C) of your population-size

estimates. To determine accuracy of your population-size estimates, you should first count every

single living beetle (both marked and unmarked) in your colony dish and then compare that number

with your calculated estimate(s).

Points to Ponder

After you have finished counting, consider the following questions:

1. Among the counters in your class, which person’s point estimate was closest to the actual

population size? Which person’s estimate was farthest?

2. Among the counters in your class, which person’s confidence interval was the narrowest?

Which person generated the widest 95% confidence interval?

3. Identify any specific factors in your class’s counting method that may have compromised the

validity of your estimate of population size.

4. Which person and which group obtained the “best” estimate of population size? (The class as a

whole should decide on criteria for “best” estimate.)

5. Of the three variables—that is, C, M, and R—required to obtain a Petersen estimate of

population size (N

EST

), which variable ought to be maximized? Please explain your conclusion.

Literature Cited (for Student Outline)

Brown, L., and J.F. Downhower. 1988. Analyses in Behavioral Ecology: A Manual for Lab and

Field. Sinauer Associates, Sunderland, Massachusetts.

Haag, M., and W.M. Tonn. 1998. Sampling density estimation and spatial relationships. Pages 197-

216, in Tested Studies for Laboratory Teaching, Volume 19 (S.J. Karcher, Editor). Proceedings

of the 19

Workshop/Conference of the Assocation for Biology Laboratory Education, 365

pages.

Krebs, C.J. 1989. Ecological Methodology. Harper and Row, New York.

Lebreton, J.-D., K.P. Burnham, J. Clobert, and D.R. Anderson. 1992. Modeling survival and testing

biological hypotheses using marked animals: A unified approach with case studies. Ecological

Monographs, 62:67-118.

Schtickzelle, N., M. Baguette, and E. Le Boulenge. 2003. Modeling insect demography from

capture-recapture data: Comparison between the constrained linear models and the Jolly-Seber

analytical method. The Canadian Entomologist, 135:313-323.

Schwarz, C.J., and G.A.F. Seber. 1999. A review of estimating animal abundance. Statistical

Science, 14:427-456.

Sokal, R.R., and F.J. Rohlf. 1981. Biometry, 2

edition. W.H. Freeman, San Francisco.

Mark-recapture census of C. maculatus populations

203

Appendix A: Building Poisson 95% Confidence Intervals

Poisson 95% confidence intervals are based on a Poisson discrete frequency distribution,

described mathematically as follows:

 e



where  is the true mean number of marked organisms in the 2

(recapture) sample, R is the number

of recaptured (marked) beetles, e is Euler’s number (or base of the natural logarithm = 2.78128…),

and P

is the probability of recapturing a (marked) beetle. Since our interest is in two-tailed 95%

confidence intervals, P

is 0.025 and 0.975. To find the Poisson 95% confidence interval for our

observed R, we would need to solve the above equation to obtain theoretical values of R that

correspond to the upper and lower 95% confidence limits.

Fortunately, statisticians saved us from all that hassle. The following table (modified from

Appendix 1.2 of Krebs [1989]) provides the lower and upper Poisson 95% confidence limits for an

observed R, or the number of recaptured beetles, in the companion spreadsheet, “PopEst.xls.”

To construct Poisson 95% confidence intervals for your population-size estimate, look in the

table below and along the column labeled “R” for the number corresponding to your observed R.

The two columns to the right of each R in the table correspond to the lower and upper limits of your

observed R. Enter these lower and upper R values one-at-a-time in the PopEst.xls spreadsheet.

Excel will then calculate N

EST

values at the upper and lower 95% confidence limits, using the

Petersen population estimation equations.

R Lower Upper R Lower Upper R Lower Upper R Lower Upper

1 0.051 5.323 26 16.77 37.67 51 37.67 66.76 76 58.84 94.23

2 0.355 6.686 27 17.63 38.16 52 38.16 66.76 77 60.24 94.70

3 0.818 8.102 28 19.05 39.76 53 39.76 68.10 78 61.90 96.06

4 1.366 9.598 29 19.05 40.94 54 40.94 69.62 79 62.81 97.54

5 1.970 11.177 30 20.33 41.75 55 40.94 71.09 80 62.81 99.17

6 2.613 12.817 31 21.36 43.45 56 41.75 71.28 81 63.49 99.17

7 3.285 13.765 32 21.36 44.26 57 43.45 72.66 82 64.95 100.32

8 3.285 14.921 33 22.94 45.28 58 44.26 74.22 83 66.76 101.71

9 4.460 16.768 34 23.76 47.02 59 44.26 75.49 84 66.76 103.31

10 5.323 17.633 35 23.76 47.69 60 45.28 75.78 85 66.76 104.40

11 5.323 19.050 36 25.40 48.74 61 47.02 77.16 86 68.10 104.58

12 6.686 20.335 37 26.31 50.42 62 47.69 78.73 87 69.62 105.90

13 6.686 21.364 38 26.31 51.29 63 47.69 79.98 88 71.09 107.32

14 8.102 22.945 39 27.73 52.15 64 48.74 80.25 89 71.09 109.11

15 8.102 23.762 40 28.97 53.72 65 50.42 81.61 90 71.28 109.61

16 9.598 25.400 41 28.97 54.99 66 51.29 83.14 91 72.66 110.11

17 9.598 26.306 42 30.02 55.51 67 51.29 84.57 92 74.22 111.44

18 11.177 27.735 43 31.67 56.99 68 52.15 84.67 93 75.49 112.87

19 11.177 28.966 44 31.67 58.72 69 53.72 86.01 94 75.49 114.84

20 12.817 30.017 45 32.28 58.84 70 54.99 87.48 95 75.78 114.84

21 12.817 31.675 46 34.05 60.24 71 54.99 89.23 96 77.16 115.60

22 13.765 32.277 47 34.66 61.90 72 55.51 89.23 97 78.73 116.93

23 14.921 34.048 48 34.66 62.81 73 56.99 90.37 98 79.98 118.35

24 14.921 34.665 49 36.03 63.49 74 58.72 93.48 99 79.98 120.36

25 16.768 36.030 50 37.67 64.95 75 58.72 93.48 100 80.25 120.36

204 Mark-recapture census of C. maculatus populations

Appendix B: Correction for Small Sample Size

Krebs (1989, Ch. 2) provides a way to correct for a theoretically upwardly biased population-size

estimate. This bias can be quite significant with small populations, or rather when the sum of

marked animals and the number of animals in the 2

(recapture) sample is greater than the actual

population size: (M+C) > N

TRUE

(Krebs, 1989: 17). Instead of using

EST

M  C

, add 1 to each of

the terms on the right side of the equation, and then subtract 1 from the quotient:



EST

(M +1)  (C + 1)

R+1

1

. If you elect to use the bias-corrected N, you should also make the

corresponding changes in the “PopEst.xls” file.

Appendix C: Accuracy Versus Precision

While counting might seem like a straightforward academic exercise, obtaining a reliable count

is an important skill to have, particularly when conducting a population census. A reliable

population size estimate is one that minimizes bias by maximizing both accuracy and precision:

high reliability = low bias = (high accuracy + high precision).

Accuracy addresses the proximity, or “near-ness,” of a point estimate to the true value of

population size. For example, if the true abundance of animals in a study population is 119, then a

point estimate of 150 animals is more accurate than one of 190. In most real-world cases, we cannot

count every individual in our study population; and without knowledge of the true population size,

we cannot evaluate accuracy of a population estimate. We are then left with the second, more useful

parameter of reliability – precision.

Because they depend on statistical variance, measures of precision address uncertainty in a

population estimate. The greater the statistical “noise” around a point estimate, the wider the error

bars that we must fit around that estimate, and the more choices of point estimates that could

correspond to the actual population size. For example, in our census study, we build 95%

confidence intervals to obtain a range of values that have equal probability of representing the true

total number of beetles in our study population. More importantly, such confidence intervals allow

us to eliminate values from an infinite universe of population-size estimates, since values lying

beyond the limits of our confidence interval are less likely to correspond to the true population size

compared to values falling within the confidence limits. In a counter-intuitive yet scientific sense,

confidence intervals tell us what population size most likely is not! Therefore, unlike with accuracy,

we can and should always evaluate precision of our population-size estimates; and we can evaluate

precision – and, hence, reliability – of our estimates with confidence intervals.

Mark-recapture census of C. maculatus populations

205

Materials (one per student group, unless noted otherwise)

• bottle of quick-drying nail polish, e.g.

Revlon™ Swoop 260 (orange-red) or some

other brightly colored nail polish

• bottle of nail-polish remover or isopropyl

(=rubbing) alcohol

• paper towels and/or Kimwipes®

• mechanical clicker counter

• stopwatch or countdown timer

• pair of soft forceps, e.g. Bioquip

featherweight forceps (Catalog No. 4748), one

per student

• organically grown mung beans (Vigna

radiata), about 1/3 cup

• 150x25-mm plastic petri plate and cover

• 100-200 adult beetles (Callosobruchus

maculatus)

• computer with Microsoft

Excel

(for data

analysis)

Notes to the Instructor

Culturing Callosobruchus maculatus

Mung beans should be pesticide-free and free of any bean-burrowing insects. We purchase pre-

packaged, organically grown mung beans from a local natural foods store.

We initiate colonies of C. maculatus beetles by placing about 10 males and 10 females into a

150x25-mm petri dish covered with a layer of mung beans. Laboratory stocks are kept on a 12-hour

daily light cycle (DLC) and at 25°C year-round. Every two months, we establish new colony plates

with individuals from existing colonies and fresh mung beans (for oviposition). Cultures should be

started two months in advance of expected use for this study to ensure sufficient numbers of adult

beetles. The ideal number of adults in a culture dish for this study is 100-200.

Recently, we experimented with alternative rearing environments. By isolating and incubating

eggs at 14-hour DLC and 30°C, we obtained acceptable egg-to-adult survival (approx. 65% across

sexes) and, more importantly, predictably short egg-to-adult development time (Table 3).

Table 3. Summary statistics on the life cycle of unmated C. maculatus individuals cultured

and maintained in isolation.

Sex

Mean + SE (sample N)

Egg-to-Adult

Development Time @ 30°C

Mean+SE (sample N)

Adult Longevity @ 25°C

Virgin Female 28.1 + 1.39 (22) days 25.1 + 0.74 (54) days

Virgin Male 28.6 + 0.38 (31) days 21.1 + 0.57 (62) days

Because C. maculatus adults appear to abstain from normal feeding (Messina, 1991; Fox et al.,

1995; Eady et al., 2000; but see Fox, 1993), males and females cannot replenish nutritional stores

spent during copulation and oviposition. With cumulative loss of mass, beetles allowed to mate and

oviposit have lifespans closer to 14 days post-eclosion (Olvido and Blumer, unpublished data).

Thus, when kept in colony plates, egg-to-egg generation time of C. maculatus can be as short as 27

days. Population sampling should take place within 12 days after the first adults have emerged.

206 Mark-recapture census of C. maculatus populations

Marking Techniques

The process of marking C. maculatus individuals presents several logistical challenges, one of

which stems from the insect’s small size (approx. 2 mm anterior-posterior length). Students can use

the brush applicator that is included with each bottle of nail polish, provided you (i.e. instructor) trim

the brush to a few hairs. Alternatively, we recommend you substitute a flat toothpick for a fine-point

brush when marking C. maculatus individuals.

Once you have decided on the appropriate marking tool, you should apply a small but visible

mark on or as near as possible to the beetle’s thorax. It is best to have students aim for the white dot

on the thorax of C. maculatus, and to caution students against applying marks that may hinder the

natural mobility of the insect. For example, instruct students to avoid painting over the beetle’s

head.

A number of participants at the A.B.L.E. 2004 workshop had trouble applying nail polish to C.

maculatus. To address these issues, the workshop participants suggested alternative methods for

marking these small animals. Below, we summarize the main advantages and disadvantages of

different techniques for marking C. maculatus and other small terrestrial arthropods, and encourage

instructors to experiment with each method (Table 4). By no means is this list exhaustive, so we

also encourage instructors to send us their comments on other alternatives for inclusion in future

revisions of this laboratory study.

Another logistical challenge in marking C. maculatus stems from the insect’s relentless effort to

hide, especially when perturbed. The more active the beetles are, the more difficulty students will

have in applying marks to the beetle’s thorax. If cooling the entire classroom to 20°C seems

impractical, then you might try cooling only the petri dish containing the sample of beetles. For

example, you could place the population dish in a refrigerator (4°C) for about 5 minutes just before

marking them. Alternatively, you could place the population dish on a flat bed of ice cubes during

the marking period.

While C. maculatus is a hardy and durable insect, students should handle these beetles carefully.

We use BioQuip

featherweight forceps because they allow for a firm grip of insect specimens

without injuring them. Surprisingly, students still manage to maim – and, in a few cases,

accidentally crush – beetles when using soft-grip forceps. Hence, we strongly recommend that you

remind students to squeeze the forceps as near as possible to the pivot point joining the two arms of

the forceps before allowing students to handle beetles. As an alternative to using forceps, students

might consider using a medium- or fine-point brush to separate beetles from mung beans during the

counting period.

Mark-recapture census of C. maculatus populations

207

Table 2. Summary of four basic marking techniques for C. maculatus adults.

Type of

Marking

Brief

Description Advantages Disadvantages

(1) Quick-drying

paint

•

described above •

paint dries quickly and

permanently; small

chance of marking non-

target animals

•

paint may dry too quickly, and

marked animal may get fixed

to a substrate or another

animal; students are likely to

smother target animal with

paint, thus hindering mobility;

clean-up can be challenging

(2) Felt-tip pen •

like (1), but marks are

applied with lightly

colored felt-tip pen

•

more precise and less

messy than (1) in the

application of marks

•

difficult to see mark; some

aromatic inks, e.g. in xylene-

based pens, may prove toxic to

insects (though C. maculatus

seems to tolerate marks from

our MonAmi® alcohol-based

pen)

(3) Fluorescent

dust

•

target animal thrown into

a shallow bath of

fluorescent dust, and then

allowed to walk off the

excess dust from itself

•

requires minimal effort

in marking, and easier to

implement than either

(1) or (2)

•

great potential for confusing

marked and unmarked

animals, as dust easily

transfers to non-target animals;

high potential for losing marks

(4) “Invisible”

dust

•

target and non-target

animals thrown into

separate baths of invisible

dust types, both of which

appear white under

visible light but

differently colored under

UV-A, or “black light”

•

same as in (3), with

additional advantage that

marks have equal effect

on both target and non-

target animals; novelty

and “pop culture” appeal

of black lights

•

same as in (3); dust marks can

easily be exchanged between

target and non-target animals;

possible safety issues when

working with UV light sources

Containment Issues

The cover of a colony petri dish (or any high-walled container) provides a useful container for

temporarily housing captured beetles. Essentially, students count as a working pair—one to transfer

beetles from the population dish to the plastic holding container, and the other to keep captured

beetles inside the container. It is important to emphasize to students in each working pair that they

should not sample the population dish at the same time; rather, one and only one student should

focus on sampling beetles from the population dish while the other student focuses on beetle

containment and recording counts. Later, the students in that working pair switch duties, so that

both can gain experience with each aspect of sampling.

Adult C. maculatus seem averse to open environments and flat surfaces (A.E. Olvido, personal

observation), so you can easily contain counted beetles by providing them with several mung beans

to which they can cling and hide beneath. You should instruct students to keep beetles in the

holding container by using a flat toothpick (or other pointed object or dry paint brush) to dislodge

beetles crawling on or near the rim of the container. We have found it useful to smear a generous

amount of Vicks™ petroleum gel around the inside rim of the holding container; we wipe away as

208 Mark-recapture census of C. maculatus populations

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

012345678

Sampling Group Number

Estimated Population Size

Estimated N

Actual N

much of the gel from the rim of the holding container before returning counted beetles to the

population dish.

Probable Causes of Sampling Bias

An important assumption in any mark-recapture method is random sampling. As explained in

the student outline, the hallmark of random sampling is independence of sampled events: Students

sample randomly when they capture a beetle (marked or unmarked) without significantly affecting

the probability of subsequent captures of marked or unmarked beetles, leading to unbiased estimates

of population size. However, results from the A.B.L.E. 2004 workshop show that the Petersen

technique as applied in this study generally yields downwardly biased point estimates of population

size (Fig. 1). A possible cause of this bias may be non-random sampling, such as when students use

the visible marks to capture beetles, which results in a higher-than-expected recapture rate. To

address the hypothesis that census marks act as visual cues that significantly increase recapture rates

(hence, downwardly biasing population-size estimates), we completed a simulated population census

using inanimate Lego™ blocks.

Figure 1. An

evaluation of bias in

Petersen estimates

of population size by

A.B.L.E. 2004

workshop

participants. Error

bars indicate

Poisson 95%

confidence intervals.

Our simulated population consisted of exactly 624 Lego™ blocks with various colors and shapes

(Table 5):

Table 5. Composition of our Lego™ population.

1x2 1x3 1x4 1x6 2x2 2x3 2x4 Total

BLUE 46 20 32 6 24 10 18 156

RED 46 20 32 6 24 10 18 156

WHITE 46 20 32 6 24 10 18 156

YELLOW 46 20 32 6 24 10 18 156

Total 184 80 128 24 96 40 72 624

Mark-recapture census of C. maculatus populations

209

We then selectively applied marks to an individual series of Lego™ blocks of different colors

and shapes, so that the exact probability of recapture in this population was known for both control

(i.e., blind sampling) and experimental treatments (i.e. color and/or shape visual cues). After several

rounds of sampling, we obtained results confirming that visually guided sampling can result in

higher-than-expected recapture rates, and consequently lower estimates of population size (Fig. 2).

Aside from random sampling, the Petersen technique and other mark-recapture census methods

also assume equal sampling effort between mark and recapture samples. In this study, we allow

students only 2 minutes to capture and count beetles. However, there are other ways to standardize

sampling effort. Instead of a 2-minute sampling window, for example, students can opt to sample by

absolute count, such that the number of beetles they mark and release (i.e., the 1

sample, or “M”

group) equals the number of beetles that they subsequently catch (in the 2

sample, or “C” group).

A third type of sampling method – yet untested – would be to sample beetles by volume: Students

use a measuring spoon to scoop up a mixture of beetles and beans of a standard volume for both 1

and 2

samples. This “volume sampling” method, of course, presumes a homogeneous distribution

of marked beetles.

-600

-500

-400

-300

-200

-100

100

200

300

Accuracy

None (Control)

Shape: 1x6

Color: Blue

Color: Red

Color: White

(21)

(9) (9) (9) (10)

Visual Cue

Figure 2. Visually guided sampling yields downwardly biased estimates of population size in

a simulation of Petersen mark-recapture sampling (F

4,53

= 5.88, P < 0.001, 1-beta = 0.981).

Mean accuracy (+/- 1 SE) was measured as the difference between estimated population size

EST

) and actual population size (N

TRUE

). Numbers in parentheses indicate number of non-

zero N

EST

for that treatment.

210 Mark-recapture census of C. maculatus populations

Using Excel™, we calculated N

EST

for various combinations of M, C, and R to illustrate the

relationship between sampling effort, recapture rate, and accuracy. Given our simulated population

of exactly 624 Lego™ blocks, we can ask “From the Petersen equation [shown in the student

outline], what is the combination of M, C, and R that generates the most accurate N

EST

?” The

answer appears as a series of M-C-R combinations (Fig. 3).

Knowing the precise relationship among the variables in the Petersen equation will guide you in

adjusting the written protocol for this study to suit your students’ sampling abilities and to work with

classroom time constraints. For example, let’s assume a true population size of 624 beetles, i.e., the

same as our population of Lego™ blocks: If students demonstrate a certain facility in capturing C.

maculatus adults, you might suggest that students strive to mark and release 50 beetles (M=50), then

randomly sample 50 beetles (C=50). A ratio of marked-to-recaptured beetles (M/R) that yields the

most accurate N

EST

would then be approximately 13.0, or one recapture for every 13 beetles

originally marked and released (Fig. 3). Thus, a sample size of 50 for both M and C groups would

suffice in possibly obtaining accurate estimates of population size, whereas a sample size of less than

624

1248

1872

2496

3120

3744

4368

4992

5616

6240

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00

Ratio (M/R)

Estimated Population Size

C=80

C=10

C=20

C=30

C=40

C=50

C=60

C=70

Figure 3. A graphical guide to sampling effort based on simulations of Petersen population-

size estimation. The horizontal dashed line indicates the known population size.

Mark-recapture census of C. maculatus populations

211

13 guarantees an inaccurate estimate. Note that absence of recaptures precludes estimation of

population size (Fig. 3).

If, on the other hand, students show less manual dexterity (or self-motivation), you might suggest

that they mark and release only 30 beetles (M=30), and later sample 30 beetles (C=30). Depending

on how randomly they sampled, you should expect an M/R ratio of approximately 22 (one recapture

per 22 beetles originally marked and released) for a reasonably accurate population-size estimate

(Fig. 3).

One Final Tip

As indicated in the student outline, students assess accuracy by counting all living beetles in their

population dish. You can facilitate accurate counts by using a sieve to separate beetles from mung

beans. At Morehouse College, we’ve fashioned our own sieves by hand-drilling 1/8-inch holes in

150 x 25 cm petri dish covers. You might be able to save yourself time and effort by purchasing

wire-mesh sieves from vendors that offer soil analysis tools, e.g., Carolina Biological or Ben

Meadows. Sieve designations of Nos. 5, 6, or 7 – corresponding to diameter openings of 4.00 mm,

3.35 mm, and 2.80 mm, respectively (consult URL http://www.wovenwire.com/reference/screen-

sieve-pr.htm for other sizes) – appear to have the appropriately sized openings for productive

sieving.

Literature Cited (for Notes to the Instructor)

Eady, P.E, N. Wilson, and M. Jackson. 2000. Copulating with multiple mates enhances female

fecundity but not egg-to-adult survival in the bruchid beetle, Callosobruchus maculatus.

Evolution, 54:2161-2165.

Fox, C.W. 1993. Multiple mating, lifetime fecundity and female mortaility of the bruchid beetle,

Callosobruchus maculatus (Coleoptera: Bruchidae). Functional Ecology, 7:203-208.

Fox, C.W., D.L. Hickman, E.L. Raleigh, and T.A. Mousseau. 1995. Paternal investment in a seed

beetle (Coleoptera: Bruchidae): Influence of male size, age, and mating history. Annals of the

Entomological Society of America, 88:100-103.

Messina, F.J. 1991. Life-history variation in a seed beetle: Adult egg-laying vs. larval competitive

ability. Oecologia (Berlin), 85:447-455.

Acknowledgements

We thank the Center for Behavioral Neuroscience (S.T.C. Program of the National Science

Foundation under Agreement No. IBN-9876754) for partial funding to develop this laboratory lesson

and the A.B.L.E. 2004 workshop participants for their spirited testing and constructive comments.